Introduction
The gradient of a line is determined by the ratio of vertical change to horizontal change.
Task
From the given link that redirect you to the pdf questions, solve the following questions
1. Find the gradient of the line AC.(no 3)
2. Find the gradient of AB.(no 8)
3. (a) Draw the graph y = 4x + 2 on the grid above(no 11)
(b) Work out the gradient of the line y = 4x + 2 (no 11)
https://corbettmaths.files.wordpress.com/2013/02/gradient-pdf.pdf
You are urged to send answers to lwandolwando59@gmail.com for marking and memo.
Process
GRADIENT
Gradient (mm) describes the slope or steepness of the line joining two points. In the figure below, line OQ is the least steep and line OT is the steepest.
To derive the formula for gradient, we consider any right-angled triangle formed from A(x1;y1) and B(x2;y2) with hypotenuse AB as shown in the diagram below. The gradient is determined by the ratio of the length of the vertical side of the triangle to the length of the horizontal side of the triangle. The length of the vertical side of the triangle is the difference in y-values of points A and B. The length of the horizontal side of the triangle is the difference in x-values of points A and B.
STEPS TO SOLVE GRADIENT
- Draw a sketch (If given Points or Equation)
- Assign values to (x1;y1) and (x2;y2)
- Write down the formula for gradient (m= change in y-values/change in x-values
- Substitute known values(to the formula)
- Write the final answer
More explanation can be found in these links:
1. https://intl.siyavula.com/read/maths/grade-10/analytical-geometry/08-analytical-geometry-02
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Evaluation
| Poor | Fair | Good | Excellent | |
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Graphing Graph using slope and y-intercept |
Graphs are not accurate. No points are visible on the graph. Confused. | Graphed 2 of the equations accurately using the y-intercept and slope. It has at least 3 points visible on the graph. Show some understanding. |
Graphed 3 of the equations accurately using the y-intercept and the slope. It has at least 3 points visible on the graph. Shows understanding. |
Graphed 4 of the equations accurately using the y-intercept and the slope. I has a least 3 points visible on the graph. Shows complete understanding. |
|
Equation of a Line Write an equation of a line with the given slope and y-intercept |
It is not clear about which number represents the slope and which one represent the y-intercept. At least 1 equation was written correctly. | Made few errors identifying the slope and the y- intercept. At least 2 equations were written correctly. |
Made minimal errors identifying the slope and the y- intercept. At least 3 equations were written correctly. |
The 4 equations are written correctly using slope and y-intercept. |
|
Slope -Intercept Form Write the slope intercept form of the equation for a line. |
Was able to identify the slope and the y-intercept on only 1 equation. |
Was able to identify the slope and the y-intercept on only 2 equations | Was able to identify the slope and the y-intercept on only 3 equations. | Was able to identify the slope and the y-intercept on all equations. |
|
Slope and y-intercept Find the slope and the y-intercept of each equation. |
Was able to identify the slope and the y-intercept of 1 of lines. Showed work. |
Was able to identify the slope and the y-intercept of 2 of the lines. Showed work. |
Was able to identify the slope and the y-intercept from 3 of the lines. Showed work. |
Was able to identify the slope and the y-intercept on all the lines. Showed work. |
Conclusion
In mathematics, the gradient is the measure of the steepness of a straight line. A gradient can be uphill in direction (from left to right) or downhill in direction (from right to left). Gradients can be positive or negative and do not need to be a whole number. The gradient of any line or curve tells us the rate of change of one variable with respect to another. This is a vital concept in all mathematical sciences. Any system that changes will be described using rates of change that can be visualised as gradients of mathematical functions
